Re: More math stuff, truth and social reality

From: Matt Gutting (tchrmatt_at_yahoo.com)
Date: 03/08/05 

Date: Mon, 07 Mar 2005 21:58:22 -0500

jstevh@msn.com wrote:
> Matt Gutting wrote:
>
>>I don't generally respond to your postings, James especially the
>>non-mathematical ones; but I felt compelled to say something in
>>response to this.
>>
>
>
> Ok.
>
>
>>jstevh@msn.com wrote:
>>
>>>One thing that I learned from my misadventures and adventures in
>
> the
>
>>>area of amateur pursuit of mathematical discoveries is that the
>
> truth
>
>>>doesn't help you much.
>>>
>>>There are any number of ways I can demonstrate the validity and
>>>importance of my work across a number of areas, from prime number
>>>research to advanced algebraic number theory, to now, factoring,
>
> where
>
>>>the math people have basically set up one criteria to block the
>
> proofs:
>
>>>They deny.
>>>
>>
>>Assuming you have the truth, denial is indeed wrong and indeed
>
> foolish.
>
>>However, the mere fact that so *many* people have detected so many
>
> errors
>
>>in so many areas of your work is generally thought to be a good
>
> (although
>
>>not perfect) indicator that there *are*, in fact, serious flaws in
>
> your
>
>>work. In other words, it is not clear to me, nor (apparently) to many
>>others, that you have in fact demonstrated the validity of your work
>>in any of the aforementioned areas.
>>
>
>
> Well, except that I myself admit to having made many errors and point
> out that I use brainstorming, where you generate lots of ideas during
> one period, and then come back to critique them.
>
> Basically I brainstorm on Usenet, where some ideas can be critiqued by
> others, and after the brainstorming period I go through the ideas
> myself very carefully.
>
> So, it's a given that there will be many errors, but my issue is with
> proven results where clearly math people are not only lying, but going
> to a lot of effort to push one point of view, like harping on errors
> when I acknowledge errors myself, without telling the rest of the
> story.

It is understood that you admit to having made many errors; although I
must point out that a number of people whose opinions seem trustworthy
independent of their interactions with you seem to feel that you've made
more errors than you have admitted to. In particular, you apparently feel
that you have "proven results" in some areas. In the area of surrogate
factoring, for example, you have claimed that your method is at least as
fast as other efficient factoring algorithms. So far we have not seen
a proof of this. I don't see evidence of lying, given that you have not
given evidence that your claim (specifically, of high speed for your
algorithm) is in fact the truth.

People certainly see and acknowledge "the rest of the story", perhaps more
than you allow yourself to admit. The errors they harp on are areas in
which they still see problems; it is not unreasonable to believe that they
have a point.

>
> Modern problem solving techniques are real, and brainstorming is real.
>
> Acting like it's not is just a blatant lie.
>

Again, I see no evidence that the posters to sci.math pretend that
brainstorming and similar approaches are nonexistent or worthless.
In my understanding, they simply seem to feel that although you say
that you are brainstorming, your results are not generally presented
with that caveat.

>
>>>To break through, notice, I have to have the best and fastest out
>>>there.
>>>
>>>If I can't *personally* build the fastest prime counting function
>
> ever,
>
>>>they act like my work should be dismissed.
>>>
>>>If I can't factor better than anything else out there, they act
>
> like my
>
>>>factoring research should be ignored.
>>>
>>
>>To the best of my understanding, this is not what the great majority
>
> of
>
>>people are saying. With respect to your factoring work in particular,
>>people don't seem to be requesting you to provide an algorithm that
>
> factors
>
>>faster and better than any others; most of them are simply asking you
>
> to
>
>>provide an algorithm. If you have, indeed, provided one which these
>
> posters
>
>>are missing or ignoring, it is your obligation to point out that
>
> algorithm
>
>>very very clearly indeed. Many posters have implemented algorithms
>
> which
>
>>they *believe* reflect the mathematics you are demonstrating; these
>>posters appear not to be insisting that your algorithm be "the best
>
> and
>
>>fastest", but to be insisting that it work as well as some methods
>
> which
>
>>are generally accepted as reasonably efficient. There appears to be
>
> some
>
>>question as to whether this is in fact true.
>
>
> Well the problem is that a basic factoring method at the level I've
> found has not been found in centuries.
>
> Basically I have equations that without a doubt relate the
> factorization of one integer to the factorization of another so that
> theoretically the factorization of one can be determined by factoring
> the other.
>
> The problem has been in implementing the theory.
>
> Now *reasonable* people, especially with a method that could
> destabilize the world economy if made viable, might be at least a
> little more cautious in considering a new factoring method, but instead
> I see a lot of denial.

Again, based on my observations on the conversations that have gone on
in this forum, I don't believe that anyone is denying that you can relate
the factorization of one number to the factorization of a second, perhaps
more easily approachable, number. What they appear to be denying is that
you have presented the work in a clear enough manner that an algorithm
can *be* designed to implement it. As well, they are apparently
denying that any algorithm based on your method is efficient enough to
work as well as current algorithms. Both these objections, while possibly
wrong, certainly merit consideration - and rebuttal, if they are wrong,
backed up by solid evidence. You don't seem to have provided any.

>
> Basically the math people are saying to me--we don't care what you can
> prove theoretically but only care if you break the world economy with a
> working algorithm, and then we'll pay attention.
>
> The thing is, what if I can?
>

If you could, or if some person could, then there would indeed be some
problems (although, from various posters' remarks, perhaps not as much as
you seem to believe). It is at this point, however, that probabilistic
arguments enter: as they enter into any debate regarding encryption. People
have devised algorithms based on your theory as they understand it, as
well as on some extensions of your ideas; they have apparently not come up
with practically useful results, and consequently they have decided that
the probability of the theory ever producing a useful algorithm is so low
as to be negligible. Again, this conclusion, while possibly wrong, deserves
consideration and rebuttal. And again, you seem to have provided neither.

> What do you say then, if you wake up tomorrow or the next day and the
> stock market crashes?
>
>
>>Even an inefficient method could be theoretically useful if the
>
> reasoning
>
>>on which it was based could lead to other theoretical breakthroughs.
>
> In
>
>>this case, there again seems to be some question as to whether your
>>algorithm will in fact do this.
>>
>
>
> The *theory* is without flaw, while it's been a bit of effort trying to
> figure out how to go from theory to implementation.
>
> I think the proper analogy is to the atomic bomb.
>
> You can have the theory that energy is locked inside of atoms, and not
> be able to quite build a nuclear bomb.
>
> Over time as the details are worked out, you can possibly build that
> bomb if you have the proper tools.
>
> I have the theory for surrogate factoring which shows to mathematical
> experts that without a doubt it is a method that relates factorizations
> as I say.
>
> If I get it to work, it's so effective it will overnight render
> security methods based on factoring as a hard problem--useless.
>

You have made this claim repeatedly, but I have yet to see any specific
results that lead me to believe this theory could produce such an
algorithm. You should note the breadth of this statement: I am advancing
the hypothesis that no algorithm based on your theory could work better than
current methods, not merely that no current algorithm does.

You have, again, made claims to the contrary; but, again, there are no
indications that such a claim is anything but a guess.

> The economic impact is hard to guess but could be quite large.
>
> Even a small drop in the stock market as a result could result in
> billions of dollars lost, and for what?
>
> Just because some mathematicians refused to play by their own rules?
>
> I'm not interested in putting out a working surrogate factoring
> algorithm in public, but I find it amazing that so many of you are so
> blithely acting as if it doesn't matter if I'm correct.

I don't think anyone is blithely acting as if it doesn't matter if you
are correct; I think people are investigating, deciding that you are
correct in your general approach, creating algorithms, testing them, and
finding them worthless in comparison to other approaches. It sounds
to me as if they are, in fact, taking you very seriously indeed; they
simply don't believe that your method is as potentially useful as you
claim. Do you have good *practical* evidence to the contrary?

If, as you say, you have no interest in creating a working surrogate
factoring algorithm, I don't see how you can expect people to do more
than cursory investigations of their own without some good supporting
evidence. I would expect, and have seen, some fairly thorough attempts
to work with your approach; but given the disappointing results they
have achieved, and the lack of evidence you have provided to indicate
that a good algorithm might exist, it would be foolish for them to assume
that such an algorithm does in fact exist, and to try to discover it.

>
> I make this work, it will be like someone moving from early atomic
> theory, to a working atom bomb, with the "experts" calling them names,
> and whistling as the world goes away.
>
>

I see no evidence, and essentially no probability, of this ever happening.

Since I haven't actually posted any mathematics in this thread, I'm going
to stop now and return to my H-numbers (which you can probably look up
in Google from a year or two ago). If I find something interesting, then
I may submit it to a journal of recreational math. If I don't? Well, there's
always my wedding to plan.

Matt

> James Harris
>